H=-32t-32t^2

Solution for H=-32t-32t^2 equation:

=-32H-32H^2

We move all terms to the left:

-(-32H-32H^2)=0

We get rid of parentheses

32H^2+32H=0

a = 32; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·32·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*32}=\frac{-64}{64}
=-1
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*32}=\frac{0}{64}
=0
$